Converting tapered hair to mesh
From the Blender Manual
on taper objects.

The taper curve is evaluated along the local X axis, using the local Y axis for width control. Note also that: Tapering a curve
causes it to get thinner towards one end. You can also alter the
proportions of the Taper throughout the tapered object by
moving/scaling/rotating the control points of the Taper Object. The
Taper Object can only be another curve. Editing the handles and
control points of the Taper Object will cause the original Object to
change shape.
In order for this to work:

It must be an open curve.

The taper is applied independently to all curves of the extruded object.

Only the first curve in a Taper Object is evaluated, even if you have several separated segments.

The scaling starts at the first control point on the left and moves along the curve to the last control point on the right.

Negative scaling, (e.g. negative local Y on the taper curve) is possible as well. However, rendering artifacts may appear.

Might need to increase the curve resolution to see more detail of the taper.

With closed curves, the taper curve in Taper Object acts along the whole curve (perimeter of the object), not just the length of the
object, and varies the extrusion depth. In these cases, you want the
relative height of the Taper Object Taper curve at both ends to be the
same, so that the cyclic point (the place where the endpoint of the
curve connects to the beginning) is a smooth transition.




In the example below, Suzanne has had a simple hair system converted to curves, then a bezier curve is used as a taper object.


The geometry settings for the converted hair are below:

The hair curve also has a subdivision surface modifier to further smooth the shape after conversion.
The hair system itself is nothing special, all default settings except that the count is changed to be much less than the default 1000 (only 36)and for suzanne is using a density vertex group for emission. Also, in order to prevent the hair from detaching from the emitter due to the forces after being converted, I used emit from volume rather than faces, or vertices.
The shape of the hair is created with two forces, turbulence and vortex
In short, as long as the curve is along the correct axis, as shown in the example you should have no problem reproducing in your own project. Once satisfied with the final shape of the curves, you may convert them to mesh via Object ‣ Convert To ‣ Mesh
I have also included a finished sample file demonstrating the taper on suzanne, hopefully it will get you in the right direction.